Numerical simulation of flow and heat transfer in radially rotating microchannels
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RESEARCH PAPER
Numerical simulation of flow and heat transfer in radially rotating microchannels Pratanu Roy • N. K. Anand • Debjyoti Banerjee
Received: 22 July 2012 / Accepted: 31 January 2013 / Published online: 7 March 2013 Ó Springer-Verlag Berlin Heidelberg 2013
Abstract Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The centrifugal force and Coriolis force, arising as a consequence of the microchannel rotation, change the flow pattern significantly from the symmetric profile of a nonrotating channel. Successful design of microfluidic devices in centrifugal microfluidics depends on effectively regulating these forces in rotating microchannels. In this work, we have numerically investigated the flow and heat transfer in rotating rectangular microchannel with continuum assumption. A pressure-based finite-volume technique with a staggered grid was applied to solve the steady incompressible Navier–Stokes and energy equations. It was observed that the effect of Coriolis force was determined by the value of the non-dimensional rotational Reynolds number (Rex). By comparing the root mean square deviation of the axial velocity profiles with the approximate analytical results of purely centrifugal flow for different aspect ratios (AR = width/height), a critical rotational Reynolds number (Rex,cr) was computed. Above this value of (Rex,cr), the effect of secondary flow becomes dominant. For aspect ratios of 0.25, 0.5, 1.0, 2.0, 4.0 and 9.09, this critical rotational Reynolds number (Rex,cr) was found to be 14.0, 5.5, 3.8, 4.7, 6.5 and 10.0, respectively.
List of symbols a Width of the microchannel (m) AR Channel aspect ratio ¼ ab b Height of the microchannel (m) Cp Specific heat at constant pressure (J/kg K) Dh Hydraulic diameter of microchannel (m) dr Radial distance of inlet from the disk center (m) fapp Apparent friction factor (m/s) fc Coriolis force (=2xw) fx Centrifugal force (=x2dr) G Modified axial pressure gradient G* Reduced axial pressure gradient h Convective heat transfer coefficient (W/m2 K) k Thermal conductivity (W/m K) Kn Knudsen number L Length of the microchannel (m) Nu Nusselt number ¼ hDk h p Pressure (Pa) Ra Rayleigh number xD2 q Rex Rotational Reynolds number ¼ lh Rex,cr Re
Critical rotational Reynolds number qW Dh Reynolds number ¼ avg l x Rossby number ¼ Re Re Revolution per minute Source term in j-direction Temperature (°C) Velocities in x, y and z directions (m/s) Co-ordinates in i-direction (x, y, z for i = 1, 2, 3)
Keywords Centrifugal microfluidics Lab-on-a-CD Convection in rotating microchannel Finite-volume method Secondary flow
Ro RPM Sj T u, v, w xi
P. Roy N. K. Anand (&) D. Banerjee Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA e-mail: [email protected]
Greek symbols b Ratio of the Coriolis force to the centrifugal force k; C Eigen values x A
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